Finite automata presentable abelian groups

We give new examples of FA presentable torsion-free abelian groups. Namely, for every n ⩾ 2 , we construct a rank n indecomposable torsion-free abelian group which has an FA presentation. We also construct an FA presentation of the group ( Z , + ) 2 in which every nontrivial cyclic subgroup is not FA recognizable.